{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QNFSIGD4IMSFIZVXJ2NWOR74EE","short_pith_number":"pith:QNFSIGD4","schema_version":"1.0","canonical_sha256":"834b24187c43245466b74e9b6747fc2114a78a89b0d37f215a1440708680f08f","source":{"kind":"arxiv","id":"1709.07475","version":1},"attestation_state":"computed","paper":{"title":"Computing bases of modular forms using the graded algebra structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"John Webb, Matthew Petty, Michael Lam, Noah McClelland","submitted_at":"2017-09-21T18:24:57Z","abstract_excerpt":"We develop a new algorithm to compute a basis for $M_k(\\Gamma_0(N))$, the space of weight $k$ holomorphic modular forms on $\\Gamma_0(N)$, in the case when the graded algebra of modular forms over $\\Gamma_0(N)$ is generated at weight two. Our tests show that this algorithm significantly outperforms a commonly used algorithm which relies more heavily on modular symbols."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.07475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-21T18:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"c699b9a41ca1150d46a29fe49404359ac3a0806b8bbd202dc37d723c50b13b29","abstract_canon_sha256":"663e5826673041a30f8822ae961c3891771e58f0b8391c0372b70833af06febd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:35.698216Z","signature_b64":"J+DD9gQ4sM93H3J8dYNdl4HOHQp4Z2yGJaXEQDuBoEewqhaEF7EUV+fu7+tNSAeLxiBkuPa1+x4e0Imvxwo3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"834b24187c43245466b74e9b6747fc2114a78a89b0d37f215a1440708680f08f","last_reissued_at":"2026-05-18T00:34:35.697595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:35.697595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing bases of modular forms using the graded algebra structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"John Webb, Matthew Petty, Michael Lam, Noah McClelland","submitted_at":"2017-09-21T18:24:57Z","abstract_excerpt":"We develop a new algorithm to compute a basis for $M_k(\\Gamma_0(N))$, the space of weight $k$ holomorphic modular forms on $\\Gamma_0(N)$, in the case when the graded algebra of modular forms over $\\Gamma_0(N)$ is generated at weight two. Our tests show that this algorithm significantly outperforms a commonly used algorithm which relies more heavily on modular symbols."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07475","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.07475","created_at":"2026-05-18T00:34:35.697702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.07475v1","created_at":"2026-05-18T00:34:35.697702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07475","created_at":"2026-05-18T00:34:35.697702+00:00"},{"alias_kind":"pith_short_12","alias_value":"QNFSIGD4IMSF","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QNFSIGD4IMSFIZVX","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QNFSIGD4","created_at":"2026-05-18T12:31:39.905425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE","json":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE.json","graph_json":"https://pith.science/api/pith-number/QNFSIGD4IMSFIZVXJ2NWOR74EE/graph.json","events_json":"https://pith.science/api/pith-number/QNFSIGD4IMSFIZVXJ2NWOR74EE/events.json","paper":"https://pith.science/paper/QNFSIGD4"},"agent_actions":{"view_html":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE","download_json":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE.json","view_paper":"https://pith.science/paper/QNFSIGD4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.07475&json=true","fetch_graph":"https://pith.science/api/pith-number/QNFSIGD4IMSFIZVXJ2NWOR74EE/graph.json","fetch_events":"https://pith.science/api/pith-number/QNFSIGD4IMSFIZVXJ2NWOR74EE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE/action/storage_attestation","attest_author":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE/action/author_attestation","sign_citation":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE/action/citation_signature","submit_replication":"https://pith.science/pith/QNFSIGD4IMSFIZVXJ2NWOR74EE/action/replication_record"}},"created_at":"2026-05-18T00:34:35.697702+00:00","updated_at":"2026-05-18T00:34:35.697702+00:00"}